What is the -d/(dt)(cos(2t)) ?

The -d/(dt)(cos(2t)) is -t d/(dt)(cos(2t))-2tsin(2t)-cos(2t)+C

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Find the Derivative - d/dt cos(2t)

\int - \frac{d}{d t} (cos (2 t)) d t

- t \frac{d}{d t} (cos (2 t)) - 2 t sin (2 t) - cos (2 t) + C

Solution steps

\int - \frac{d}{d t} (cos (2 t)) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{d}{d t} (cos (2 t)) d t

Apply Integration By Parts

: t \frac{d}{d t} (cos (2 t)) - \int - 4 t cos (2 t) d t

= - (t \frac{d}{d t} (cos (2 t)) - \int - 4 t cos (2 t) d t)

\int - 4 t cos (2 t) d t = - 2 t sin (2 t) - cos (2 t)

= - (t \frac{d}{d t} (cos (2 t)) - (- 2 t sin (2 t) - cos (2 t)))

Simplify

= - t \frac{d}{d t} (cos (2 t)) - 2 t sin (2 t) - cos (2 t)

Add a constant to the solution

= - t \frac{d}{d t} (cos (2 t)) - 2 t sin (2 t) - cos (2 t) + C

- \frac{d}{d x} (2 cos (2 x))

- \frac{d}{d x} (\frac{1}{( e ^{x} )})

\frac{d y}{d x} y = x sin (x)

\frac{1}{( y ^{2} )}

- \frac{d}{d x} \frac{1}{( ( 1 - x ) ^{2} )}

What is the -d/(dt)(cos(2t)) ?
The -d/(dt)(cos(2t)) is -t d/(dt)(cos(2t))-2tsin(2t)-cos(2t)+C